Magnetic plasma filamentary structures in the spectrum of α²-dynamos

L. C. Garcia de Andrade^1,2

¹ Departamento de Física Teórica-IF, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier, 524 Cep 20550-003, Maracanã, Rio de Janeiro, RJ, Brasil
² Institute for Cosmology and Philosophy of Nature, Croatia

Abstract
Previously, Kinney et al. [4] have investigated plasma filamentary structure dynamics. Recently, Wilkin et al. [5] have shown that the kinetic energy spectrum of magnetic structures in small-scale dynamos is predominantly filamentary. Kirilov et al. [6] found that the use of boundary values of the mean-field isotropic helical turbulent α²-dynamo could determine the morphology of dynamo instability. In this paper, a filamentary structure of magnetic fields in Frenet frame diffusive media is shown to lead to kinematic chaotic dynamo in a 3D Euclidean space E³. In 2D, in agreement with the Zeldovich anti-dynamo theorem, no dynamo action spectrum is either found, or a slow dynamo action is found. Curvature and diffusion effects are encoded in the matrix representation of the α²-dynamo operator. Instead of the principal scalar curvatures κ₁ and κ₂ of the surface of structures, only one scalar curvature κ is needed to determine the dynamos spectra. The filament thickness increases with the scalar curvature, as in solar physics. Refs 18.